Back in the day we used to hold "store card swapping parties" where you'd bring your store card, drop it in the pile, and then everyone randomly picks a new one. Do it about once a month.
Now of course the store cards are tied to apps that give you coupons on things you buy, so it's more in your interest not to mess with them.
Much harder to do that with phone apps, alas.
Discussion of this: https://www.creditcards.com/credit-card-news/retailer-data-t...
I mentioned it in another comment, but the combination of PCI compliance and the use of chip+pin make it difficult for retailors to use credit cards to track an individual, but the credit card company can.
However, if the retailer then goes back and purchases the data from the credit card company, I agree, they will know who "Customer #12345" is with regards to the person.